The R&D filter kit for the 15F consists of an elbow tube extension with the filter at the end of it. The Riva Power Filter is just a filter attached to the trottle body.

What is the difference, between both? if any

Either system will provide improved performance as they both replace the restrictive stock air box. The most noticeable difference (besides being more expensive) is the R&D set-up utilizes an aluminum tube to move the filter/air inlet away from the throttle body. We tested several designs and found the only way to gain from doing this is to move the filter all the way to the front of the craft. But doing so would significantly increase the cost. While heat is the enemy of performance, the Kawi's don't seem to be affected by it as much as the Doo's. So we opted to go with a simpler, less costly set-up that provides the most for the money as well as opening up the engine compartment.

Ok, looking at the engine, I can see one or two hoses coming from the engine and attached to the OEM Airbox, correct me if I'm wrong.
What I have to do with those hoses?

Those are breather hoses for the engine. We provide two small K&N filters that install into them. You then secure them to the engine with zip ties.